Size: px
Start display at page:

Download ""

Transcription

1 AP Physics 1- Torque, Rotational Inertia, and Angular Momentum Practice Problems FACT: The center of mass of a system of objects obeys Newton s second law- F = Ma cm. Usually the location of the center of mass (cm) is obvious, but for several objects is expressed as: Mx cm = m 1 x 1 + m 2 x 2 + m 3 x 3, where M is the sum of the masses in the expression. In some cases the center of mass is not located on the body of the object. When an object or system rotates, it will usually rotate around its center of mass. Expect 1-2 questions covering this topic on the AP Exam. Q1. A 59-kg woman and a 71-kg man sit on a seesaw, 3.5 m long. Where is their center of mass? Q2. A fisherman in a boat catches a great white shark with a harpoon. The shark struggles for a while and then becomes limp when at a distance of 300 m from the boat. The fisherman pulls the shark by the rope attached to the harpoon. During this operation, the boat (initially at rest) moves 45 m in the direction of the shark. The mass of the boat is 5400 kg. What is the mass of the shark? Pretend that the water exerts no friction. Q3. A 70-kg man is standing on the end of a 250-kg log that is floating in the water. Both the man and the log are at rest, and the log is 3.0 m long. If the man walks to the other end of the log, how far will the log move in the water? Ignore any forces exerted on the log by the water. FACT: Torque (Ƭ) is a force that causes an object to turn or rotate. It is a measure of a force s ability to cause an object to accelerate rotationally. If an object is initially at rest, and then starts to spin, something must have exerted a net torque. If an object is initially spinning, it would require a net torque to stop spinning. FACT: We use sine for torque problems because the torque is a perpendicular force causing an angular acceleration. By definition, the cross product of the force and the moment arm (lever arm, line of action) is the torque. The units for torque are N.m, which is not referred to as a Joule. Notice that sine (90) = 1. Recall we used cosine in work problems because the force applied resulting in work is directly correlated with the displacement of the object. In this case, cosine (180) =1. Please study the diagrams below and note that Ƭ = Fr sin θ = r F = rf sin θ = F r. The lever arm is the perpendicular distance from the axis of rotation to the point where the force is applied. You can also think of torque as the component of the force perpendicular to the lever arm multiplied by the distance (r).

2 Q4: A captain of a ship turns the stirring wheel by applying a 20 N toque. If he applies the force at a radius of 0.2 m from the axis of rotation, at an angle of 80 degrees to the line of action (moment arm), what torque does he apply? Q5: A mechanic tightens the lugs on a tire by applying a torque of 110 Nm at an angle of 90 degrees to the moment arm. What force is applied if the wrench is 0.4 m long? What is the minimum length if the wrench if the mechanic is only capable of applying a force of 200N? Q6. A constant force F is applied for five seconds at various points of the object, as shown in the diagram. Rank the magnitude of the torque exerted by the force on the object about an axle located at the center of mass from smallest to largest. Q7. A student pulls down on a small modified Atwood machine with a force of 30 N, as shown in the diagram. What is the torque of this force? FACT: An object will not rotate if the net torque (ƩƬ) is equal to zero. This is known as rotational equilibrium. Q8. A 15-kg box sits on a lever arm at a distance of 5 meters from the axis of rotation. What distance must a second 10-kg box sit to create a clockwise moment that will result in a net torque of zero? What would occur if the moment arm of the second box was 8 m? 15 kg Q9. Forces are applied along various points on a lever arm as shown. Calculate the net torque and describe the resulting motion of the lever. Determine the force and distance from the axis of rotation that would result in a net moment (torque) of zero. FACT: In torque problems with a large extended object (table, bridge, pole, ladder) do not forget that the lever arm itself will have a mass and a center of mass (cm). It is acceptable to assume the object s weight is all hanging from the cm. Q10. A 3-kg Academy sign is hung from a 1-kg, 4-meter horizontal pole as shown. The sign is hung 1-meter from the right side. A wire is attached to prevent the sign from rotating. Find the tension in the wire. FACT: In table/bridge problems the fulcrum (pivot point) is arbitrary because the object is not rotating. Choose one of the supports as the fulcrum, which means that point now has zero torque (r = 0). Q11. A table has an 18-kg object placed 0.8 meters from the left table leg. The mass of the table top is 6-kg. What is the force exerted on each leg? What would occur if the left leg broke?

3 Q12: A 50-kg box is hung from a 5-meter long, 200-kg horizontal pole as shown. A wire is attached to prevent the sign from rotating. The box and wire attach at the right end of the pole as shown below. Find the tension in the wire. FACT: A system is in static equilibrium when the sum of the forces and the sum of the torque are zero. We will also explore the idea of static equilibrium in an AP Investigation for this unit. This concept can be applied in what I call a ladder problem and you will encounter one of these problems on the AP Exam. In ladder problems, it is easier to use the perpendicular distance (r ) to find the torque. You can still use the perpendicular component of force (F ). Q13. A 5 meter, 200N-long ladder rests against a wall. The ladders center of mass is 3.0 meters up the ladder. The coefficient of friction on the ground is How far along the ladder can a 75-kg person climb before it slips? The angle between the ladder and ground is 56 degrees. Q14: Examine the diagram of a bear on a pole. The string (T) can hold a total of 900 N. Can the bear reach the 80-N basket of food without the string breaking? The total distance out to the food is 6-m. FACT: The rotational equivalent of Newton s Second Law is expressed as, ƩƬ = Iα, where I is the rotational inertia and α is the angular acceleration. The rotational inertia is sometimes referred to as the moment of inertia. Recall from translational dynamics that the larger the force, the greater the acceleration. Also, recall that the larger the mass, the smaller the acceleration (inversely proportional). This also holds true for rotational dynamics (ƩƬ = Iα); the rotational inertia is inversely related to the angular acceleration. FACT: Objects that have most of their mass near their axis of radiation have a small rotational inertia, while objects that have more mass farther from the axis of rotation have larger rotational inertias. The AP exam will provide with the formula for rotational inertias, as they are derived using calculus. Here are some of the common formulas:

4 Q15. An object with uniform mass density is rotated about an axle, which may be in position A, B, C, or D. Rank the object s rotational inertia from smallest to largest based on the axle position. FACT: For a system of objects you will need to add the rotational inertia of each object to find the rotational inertia of a system. For point masses, this can be expressed mathematically as I = Ʃmr 2. Q16. Find the rotational inertia (I) of two 5-kg bowling balls joined by a meter long rod of negligible mass when rotated about the center of the rod. Compare this to the I of the object when rotated about one of the masses. The dot indicates the axis. Q17. What is the angular acceleration experienced by a uniform solid disc of mass 2-kg and radius 0.1 m when a net torque of 10 N.m is applied? Assume the disc spins about its center. Q18. Given the net torque of the system, find the angular acceleration for the system of three particle masses. The radius from the axis of rotation is 12 m and the masses are equidistant. Assuming a constant acceleration, what would the angular velocity be after 5 seconds? How many revolutions will be completed after 20 seconds with constant acceleration? FACT: The parallel axis theorem is given as: I pa = I cm + Md 2. This can be used to find the rotational inertia of an object when the axis of rotation is not in the center of mass (cm). The equation says that the rotational inertia around a parallel axis equals the rotational inertia at the center of mass plus the total mass of the object multiplied by the distance between the two axes squared. This equation is not provided on the AP Exam, but it could prove to be very useful and has been applicable to the exam in the past. Q19. What is the rotational inertia (I) of the disk shown with a radius, R = 4 meters and a mass of 2 kg? The same disk is rotated around an axis that is 0.5 meters from the center of the disk. What is the new rotational inertia (I) of the disk? What would the rotational inertia be if the disk axis was 3.75 meters from the center? Q20. A hoop with a radius of 0.75 meters is rotated about an axis 0.5 meters from the center of mass. The hoop weighs 2 kg. What is the rotational inertia of the hoop? Q21. To the right are four identical figure L s, which are constructed from two rods of equal lengths and masses. For each figure, a different axis of rotation is indicated by the small circle with the dot inside, which indicates an axis that is perpendicular to the plane of the L s. The axis of rotation is located either at the center or one end of a rod for each figure. Rank these L figures according to their moments of inertia about the indicated axes, from largest to smallest. Ignore the width of each rod but not the length.

5 Q 22. A light string attached to a mass m is wrapped around a pulley of mass m p and radius R. If the rotational inertia of the pulley is ½m p R 2, derive an expression for the acceleration of the mass. Q23. A merry-go-round on a playground with a rotational inertia of 100 kg m 2 starts at rest and is accelerated by a force of 150N at a radius of 1m from its center. If this force is applied at an angle of 90 from the line of action for a time of 0.5 seconds, what is the final rotational velocity of the merry-go-round? Q24. Three meter-long, uniform 200-g bars each have a small 200-g mass attached to them in the positions shown on the diagram below. A person grips the bars in the locations shown and attempts to rotate the bars in the directions shown. Calculate the rotational inertia for each bar. Q25. A weight is tied to a rope that is wrapped around a pulley. The pulley is initially rotating counterclockwise and is pulling the weight up. The tension in the rope creates a torque on the pulley that opposes this rotation. a) On the axes below, draw a graph of the angular velocity versus time for the period from the initial instant shown until the weight comes back down to the same height. Take the initial angular velocity as positive. b) Draw a graph of the angular acceleration versus time for the same time period. Q26. An angler balances a fishing rod on her finger as shown. If she were to cut the rod along the dashed line, would the weight of the piece on the left hand side be greater than, less than, or equal to the weight of the piece on the right-hand side? Explain using both qualitative and quantitative reasoning.

6 Q27. Visit the Unit 6 webpage on and scroll down to the problem set for this unit. You will find an accompanying video of a wheel that is being accelerated by a falling 175-kg mass. Derive an expression for the rotational inertia of the wheel. Hint- you will need to look at the motion of the falling weight and the motion of the spinning wheel separately. FACT: Recall that linear momentum is a vector quantity (p = mv ). Recall that impulse is equal to a change in momentum, which equals a force exerted for a period of time (J = Δp = FΔt). The rotational analogue for the momentum is known as angular momentum (L = Iω). This vector describes how hard it is to stop (or start) a rotating object. Angular impulse is equal to a change in angular momentum, which equals a torque exerted for a period of time. (ΔL =Iω f -Iω o = ƬΔt). Q28. A constant force is applied for a constant time at various points on the object shown below. If point C is the axis of rotation, rank the magnitude of the change of the object s angular momentum due to the force. Rank from the smallest to the largest. FACT: The law of conservation of angular momentum states that the product of an objects rotational inertia and angular velocity (L = Iω) about the center of mass is conserved in a closed system with no external torque. As rotational inertia increases, angular velocity decreases, and thus, they are inversely proportional. Angular momentum is conserved in nearly all collisions, as well as many other situations. Q29. A disc (radius = 1 m) with a rotational inertia of 1 kg.m 2 spins about an axle through its center of mass with an angular velocity of 10 rad/s. A second disc (radius = 0.5 m), which is not turning, but has a rotational inertia of 0.25 kg.m 2 is slid along the axle until it makes contact with the first disc. If the discs stick together, what is their combined angular velocity? Q30. Sophia spins on a rotating pedestal with an angular velocity of 8 radians per second. Eric throws her an exercise ball, which increases her rotational inertia from 2 kg m 2 to 2.5 kg m 2. What is Sophia s angular velocity after catching the exercise ball? (Neglect any external torque from the ball.) FACT: For a single point particle moving in a circle around an axis, its angular momentum is L = mvr (r = radius of circle). However, a single point particle that is moving in a straight line can also have angular momentum that is relative to the point of reference (L Q = mvr sinθ or L Q = mωr 2 sinθ or L Q = pr sinθ). The subscript of Q shows that the angular momentum is relative to point Q on the schematic to the right. Q31. Four particles, each of mass M, move in the x-y plane with varying velocities as shown in the diagram. The velocity vectors are drawn to scale. Rank the magnitude of the angular momentum about the origin for each particle from largest to smallest.

7 Q32. A uniform rod of mass M is at rest on a frictionless table. A ball of Play-doh with a mass M is moving to the left, as shown in the diagram. The ball of Play-doh collides and 2 sticks to the rod. What is the speed of the center of mass of the rod-play-doh system? Q33. A planet (P) orbits the Sun (S) in an elliptical orbit. (a). Using qualitative reasoning, explain how to determine the torque exerted by the force of the Sun on the planet. (b). Using semiqualitative reasoning, explain how angular momentum is conserved in the Sunplanet system. FACT: If an object exhibits both translational and rotational motion, the total kinetic energy of the object can be found by K tot = ½ mv 2 + ½ Iω 2. The units will be Joules. Q34. A person rolls a bowling ball of mass 7 kg and radius 10.9 cm down a lane with a velocity of 6 m/s. Find the rotational kinetic energy of the bowling ball, assuming it does not slip. Find the total kinetic energy. Q35. Sophia kicks a soccer ball which rolls across a field with a velocity of 5 m/s. What is the ball s total kinetic energy? The ball has a mass of 0.43 kg, a radius of 0.11 m, and it does not slip as it rolls. The rotational inertia of a hollow sphere is 2/3 MR 2 Q36. An ice skater spins with a specific angular velocity. She brings her arms and legs closer to her body, reducing her rotational inertia to half its original value. What happens to her angular velocity? What happens to her rotational kinetic energy? Answer using semiqualitative reasoning. FACT: You can use the conservation of mechanical energy to solve rotational kinetic energy problems. Recall with conservative forces the total mechanical energy equals the potential energy (U) plus the kinetic energy (K). The major types of potential energy are springs and gravitational. Q37. Find the speed of a disc of radius 0.5 meters and mass 2-kg at the base of the incline. The disc starts at rest and rolls down the incline with a height of 5 meters without slipping. The incline makes a 20 angle with the horizontal surface. FACT: On occasion when using ƩƬ = Iα you may need to substitute Fr for torque or ω f -ω o /t for α. Q38. A hoop with rotational inertia I=0.1 kg m 2 spins about a frictionless axle with an angular velocity of 5.0 radians per second. At what radius from the center of the hoop should a force of 2.0 newtons be applied for 3 seconds in order to accelerate the hoop to an angular speed of 10 radians per second?

8 Challenge Problems (39-42): These problems are just for fun! Q39. Two ropes, having tensions T2 and T3, support a uniform 100-N beam and two weights. If the right weight has a mass of 25 kg and T2 has a tension of 500 N, calculate the tension in T3 as well as the mass of the unknown weight. 250 N; 40 kg Q40. A 75-kg block is suspended from the end of a uniform 100-N beam. If θ = 30º, what are the values of T2 as well as the horizontal and vertical forces on the hinge? Q41. A uniform bar of mass m and length L extends horizontally from a wall. A supporting wire connects the wall to the bar s midpoint, making an angle of 55 with the bar. A sign of mass M hangs from the end of the bar. If the system is in static equilibrium and the wall has friction, determine the tension in the wire and the strength of the force exerted on the bar by the wall if m = 8 kg and M = 12 kg. Q42. Two blocks are connected by a light string over a pulley of mass m p and radius R as shown in the diagram. Derive an expression for the acceleration of mass m 2 if m 1 sits on a frictionless surface.

Torque rotational force which causes a change in rotational motion. This force is defined by linear force multiplied by a radius.

Torque rotational force which causes a change in rotational motion. This force is defined by linear force multiplied by a radius. Warm up A remote-controlled car's wheel accelerates at 22.4 rad/s 2. If the wheel begins with an angular speed of 10.8 rad/s, what is the wheel's angular speed after exactly three full turns? AP Physics

More information

Big Idea 4: Interactions between systems can result in changes in those systems. Essential Knowledge 4.D.1: Torque, angular velocity, angular

Big Idea 4: Interactions between systems can result in changes in those systems. Essential Knowledge 4.D.1: Torque, angular velocity, angular Unit 7: Rotational Motion (angular kinematics, dynamics, momentum & energy) Name: Big Idea 3: The interactions of an object with other objects can be described by forces. Essential Knowledge 3.F.1: Only

More information

Chapter 9-10 Test Review

Chapter 9-10 Test Review Chapter 9-10 Test Review Chapter Summary 9.2. The Second Condition for Equilibrium Explain torque and the factors on which it depends. Describe the role of torque in rotational mechanics. 10.1. Angular

More information

= o + t = ot + ½ t 2 = o + 2

= o + t = ot + ½ t 2 = o + 2 Chapters 8-9 Rotational Kinematics and Dynamics Rotational motion Rotational motion refers to the motion of an object or system that spins about an axis. The axis of rotation is the line about which the

More information

Big Ideas 3 & 5: Circular Motion and Rotation 1 AP Physics 1

Big Ideas 3 & 5: Circular Motion and Rotation 1 AP Physics 1 Big Ideas 3 & 5: Circular Motion and Rotation 1 AP Physics 1 1. A 50-kg boy and a 40-kg girl sit on opposite ends of a 3-meter see-saw. How far from the girl should the fulcrum be placed in order for the

More information

End-of-Chapter Exercises

End-of-Chapter Exercises End-of-Chapter Exercises Exercises 1 12 are conceptual questions that are designed to see if you have understood the main concepts of the chapter. 1. Figure 11.21 shows four different cases involving a

More information

AP Physics 1 Rotational Motion Practice Test

AP Physics 1 Rotational Motion Practice Test AP Physics 1 Rotational Motion Practice Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A spinning ice skater on extremely smooth ice is able

More information

31 ROTATIONAL KINEMATICS

31 ROTATIONAL KINEMATICS 31 ROTATIONAL KINEMATICS 1. Compare and contrast circular motion and rotation? Address the following Which involves an object and which involves a system? Does an object/system in circular motion have

More information

Chapter 8, Rotational Equilibrium and Rotational Dynamics. 3. If a net torque is applied to an object, that object will experience:

Chapter 8, Rotational Equilibrium and Rotational Dynamics. 3. If a net torque is applied to an object, that object will experience: CHAPTER 8 3. If a net torque is applied to an object, that object will experience: a. a constant angular speed b. an angular acceleration c. a constant moment of inertia d. an increasing moment of inertia

More information

Circular Motion, Pt 2: Angular Dynamics. Mr. Velazquez AP/Honors Physics

Circular Motion, Pt 2: Angular Dynamics. Mr. Velazquez AP/Honors Physics Circular Motion, Pt 2: Angular Dynamics Mr. Velazquez AP/Honors Physics Formulas: Angular Kinematics (θ must be in radians): s = rθ Arc Length 360 = 2π rads = 1 rev ω = θ t = v t r Angular Velocity α av

More information

1 MR SAMPLE EXAM 3 FALL 2013

1 MR SAMPLE EXAM 3 FALL 2013 SAMPLE EXAM 3 FALL 013 1. A merry-go-round rotates from rest with an angular acceleration of 1.56 rad/s. How long does it take to rotate through the first rev? A) s B) 4 s C) 6 s D) 8 s E) 10 s. A wheel,

More information

We define angular displacement, θ, and angular velocity, ω. What's a radian?

We define angular displacement, θ, and angular velocity, ω. What's a radian? We define angular displacement, θ, and angular velocity, ω Units: θ = rad ω = rad/s What's a radian? Radian is the ratio between the length of an arc and its radius note: counterclockwise is + clockwise

More information

Rotation review packet. Name:

Rotation review packet. Name: Rotation review packet. Name:. A pulley of mass m 1 =M and radius R is mounted on frictionless bearings about a fixed axis through O. A block of equal mass m =M, suspended by a cord wrapped around the

More information

PSI AP Physics I Rotational Motion

PSI AP Physics I Rotational Motion PSI AP Physics I Rotational Motion Multiple-Choice questions 1. Which of the following is the unit for angular displacement? A. meters B. seconds C. radians D. radians per second 2. An object moves from

More information

CHAPTER 8: ROTATIONAL OF RIGID BODY PHYSICS. 1. Define Torque

CHAPTER 8: ROTATIONAL OF RIGID BODY PHYSICS. 1. Define Torque 7 1. Define Torque 2. State the conditions for equilibrium of rigid body (Hint: 2 conditions) 3. Define angular displacement 4. Define average angular velocity 5. Define instantaneous angular velocity

More information

Rolling, Torque & Angular Momentum

Rolling, Torque & Angular Momentum PHYS 101 Previous Exam Problems CHAPTER 11 Rolling, Torque & Angular Momentum Rolling motion Torque Angular momentum Conservation of angular momentum 1. A uniform hoop (ring) is rolling smoothly from the

More information

PSI AP Physics I Rotational Motion

PSI AP Physics I Rotational Motion PSI AP Physics I Rotational Motion Multiple-Choice questions 1. Which of the following is the unit for angular displacement? A. meters B. seconds C. radians D. radians per second 2. An object moves from

More information

Chapter 8 - Rotational Dynamics and Equilibrium REVIEW

Chapter 8 - Rotational Dynamics and Equilibrium REVIEW Pagpalain ka! (Good luck, in Filipino) Date Chapter 8 - Rotational Dynamics and Equilibrium REVIEW TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. 1) When a rigid body

More information

Webreview Torque and Rotation Practice Test

Webreview Torque and Rotation Practice Test Please do not write on test. ID A Webreview - 8.2 Torque and Rotation Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A 0.30-m-radius automobile

More information

Summer Physics 41 Pretest. Shorty Shorts (2 pts ea): Circle the best answer. Show work if a calculation is required.

Summer Physics 41 Pretest. Shorty Shorts (2 pts ea): Circle the best answer. Show work if a calculation is required. Summer Physics 41 Pretest Name: Shorty Shorts (2 pts ea): Circle the best answer. Show work if a calculation is required. 1. An object hangs in equilibrium suspended by two identical ropes. Which rope

More information

Physics 111. Tuesday, November 2, Rotational Dynamics Torque Angular Momentum Rotational Kinetic Energy

Physics 111. Tuesday, November 2, Rotational Dynamics Torque Angular Momentum Rotational Kinetic Energy ics Tuesday, ember 2, 2002 Ch 11: Rotational Dynamics Torque Angular Momentum Rotational Kinetic Energy Announcements Wednesday, 8-9 pm in NSC 118/119 Sunday, 6:30-8 pm in CCLIR 468 Announcements This

More information

PHYSICS 149: Lecture 21

PHYSICS 149: Lecture 21 PHYSICS 149: Lecture 21 Chapter 8: Torque and Angular Momentum 8.2 Torque 8.4 Equilibrium Revisited 8.8 Angular Momentum Lecture 21 Purdue University, Physics 149 1 Midterm Exam 2 Wednesday, April 6, 6:30

More information

Chapter 10. Rotation

Chapter 10. Rotation Chapter 10 Rotation Rotation Rotational Kinematics: Angular velocity and Angular Acceleration Rotational Kinetic Energy Moment of Inertia Newton s nd Law for Rotation Applications MFMcGraw-PHY 45 Chap_10Ha-Rotation-Revised

More information

PHYSICS 221, FALL 2011 EXAM #2 SOLUTIONS WEDNESDAY, NOVEMBER 2, 2011

PHYSICS 221, FALL 2011 EXAM #2 SOLUTIONS WEDNESDAY, NOVEMBER 2, 2011 PHYSICS 1, FALL 011 EXAM SOLUTIONS WEDNESDAY, NOVEMBER, 011 Note: The unit vectors in the +x, +y, and +z directions of a right-handed Cartesian coordinate system are î, ĵ, and ˆk, respectively. In this

More information

It will be most difficult for the ant to adhere to the wheel as it revolves past which of the four points? A) I B) II C) III D) IV

It will be most difficult for the ant to adhere to the wheel as it revolves past which of the four points? A) I B) II C) III D) IV AP Physics 1 Lesson 16 Homework Newton s First and Second Law of Rotational Motion Outcomes Define rotational inertia, torque, and center of gravity. State and explain Newton s first Law of Motion as it

More information

CHAPTER 8 TEST REVIEW MARKSCHEME

CHAPTER 8 TEST REVIEW MARKSCHEME AP PHYSICS Name: Period: Date: 50 Multiple Choice 45 Single Response 5 Multi-Response Free Response 3 Short Free Response 2 Long Free Response MULTIPLE CHOICE DEVIL PHYSICS BADDEST CLASS ON CAMPUS AP EXAM

More information

Chapter 8. Rotational Equilibrium and Rotational Dynamics. 1. Torque. 2. Torque and Equilibrium. 3. Center of Mass and Center of Gravity

Chapter 8. Rotational Equilibrium and Rotational Dynamics. 1. Torque. 2. Torque and Equilibrium. 3. Center of Mass and Center of Gravity Chapter 8 Rotational Equilibrium and Rotational Dynamics 1. Torque 2. Torque and Equilibrium 3. Center of Mass and Center of Gravity 4. Torque and angular acceleration 5. Rotational Kinetic energy 6. Angular

More information

Rotational Kinematics and Dynamics. UCVTS AIT Physics

Rotational Kinematics and Dynamics. UCVTS AIT Physics Rotational Kinematics and Dynamics UCVTS AIT Physics Angular Position Axis of rotation is the center of the disc Choose a fixed reference line Point P is at a fixed distance r from the origin Angular Position,

More information

Moment of Inertia Race

Moment of Inertia Race Review Two points, A and B, are on a disk that rotates with a uniform speed about an axis. Point A is closer to the axis than point B. Which of the following is NOT true? 1. Point B has the greater tangential

More information

1. Which of the following is the unit for angular displacement? A. Meters B. Seconds C. Radians D. Radian per second E. Inches

1. Which of the following is the unit for angular displacement? A. Meters B. Seconds C. Radians D. Radian per second E. Inches AP Physics B Practice Questions: Rotational Motion Multiple-Choice Questions 1. Which of the following is the unit for angular displacement? A. Meters B. Seconds C. Radians D. Radian per second E. Inches

More information

Name: Date: Period: AP Physics C Rotational Motion HO19

Name: Date: Period: AP Physics C Rotational Motion HO19 1.) A wheel turns with constant acceleration 0.450 rad/s 2. (9-9) Rotational Motion H19 How much time does it take to reach an angular velocity of 8.00 rad/s, starting from rest? Through how many revolutions

More information

AP Physics Multiple Choice Practice Torque

AP Physics Multiple Choice Practice Torque AP Physics Multiple Choice Practice Torque 1. A uniform meterstick of mass 0.20 kg is pivoted at the 40 cm mark. Where should one hang a mass of 0.50 kg to balance the stick? (A) 16 cm (B) 36 cm (C) 44

More information

Exam 3 Practice Solutions

Exam 3 Practice Solutions Exam 3 Practice Solutions Multiple Choice 1. A thin hoop, a solid disk, and a solid sphere, each with the same mass and radius, are at rest at the top of an inclined plane. If all three are released at

More information

TORQUE. Chapter 10 pages College Physics OpenStax Rice University AP College board Approved.

TORQUE. Chapter 10 pages College Physics OpenStax Rice University AP College board Approved. TORQUE Chapter 10 pages 343-384 College Physics OpenStax Rice University AP College board Approved. 1 SECTION 10.1 PAGE 344; ANGULAR ACCELERATION ω = Δθ Δt Where ω is velocity relative to an angle, Δθ

More information

Exercise Torque Magnitude Ranking Task. Part A

Exercise Torque Magnitude Ranking Task. Part A Exercise 10.2 Calculate the net torque about point O for the two forces applied as in the figure. The rod and both forces are in the plane of the page. Take positive torques to be counterclockwise. τ 28.0

More information

TutorBreeze.com 7. ROTATIONAL MOTION. 3. If the angular velocity of a spinning body points out of the page, then describe how is the body spinning?

TutorBreeze.com 7. ROTATIONAL MOTION. 3. If the angular velocity of a spinning body points out of the page, then describe how is the body spinning? 1. rpm is about rad/s. 7. ROTATIONAL MOTION 2. A wheel rotates with constant angular acceleration of π rad/s 2. During the time interval from t 1 to t 2, its angular displacement is π rad. At time t 2

More information

Fall 2007 RED Barcode Here Physics 105, sections 1 and 2 Please write your CID Colton

Fall 2007 RED Barcode Here Physics 105, sections 1 and 2 Please write your CID Colton Fall 007 RED Barcode Here Physics 105, sections 1 and Exam 3 Please write your CID Colton -3669 3 hour time limit. One 3 5 handwritten note card permitted (both sides). Calculators permitted. No books.

More information

Chapter 8 Rotational Motion and Equilibrium. 1. Give explanation of torque in own words after doing balance-the-torques lab as an inquiry introduction

Chapter 8 Rotational Motion and Equilibrium. 1. Give explanation of torque in own words after doing balance-the-torques lab as an inquiry introduction Chapter 8 Rotational Motion and Equilibrium Name 1. Give explanation of torque in own words after doing balance-the-torques lab as an inquiry introduction 1. The distance between a turning axis and the

More information

I pt mass = mr 2 I sphere = (2/5) mr 2 I hoop = mr 2 I disk = (1/2) mr 2 I rod (center) = (1/12) ml 2 I rod (end) = (1/3) ml 2

I pt mass = mr 2 I sphere = (2/5) mr 2 I hoop = mr 2 I disk = (1/2) mr 2 I rod (center) = (1/12) ml 2 I rod (end) = (1/3) ml 2 Fall 008 RED Barcode Here Physics 105, sections 1 and Exam 3 Please write your CID Colton -3669 3 hour time limit. One 3 5 handwritten note card permitted (both sides). Calculators permitted. No books.

More information

Rotation. PHYS 101 Previous Exam Problems CHAPTER

Rotation. PHYS 101 Previous Exam Problems CHAPTER PHYS 101 Previous Exam Problems CHAPTER 10 Rotation Rotational kinematics Rotational inertia (moment of inertia) Kinetic energy Torque Newton s 2 nd law Work, power & energy conservation 1. Assume that

More information

Rotation Quiz II, review part A

Rotation Quiz II, review part A Rotation Quiz II, review part A 1. A solid disk with a radius R rotates at a constant rate ω. Which of the following points has the greater angular velocity? A. A B. B C. C D. D E. All points have the

More information

Handout 7: Torque, angular momentum, rotational kinetic energy and rolling motion. Torque and angular momentum

Handout 7: Torque, angular momentum, rotational kinetic energy and rolling motion. Torque and angular momentum Handout 7: Torque, angular momentum, rotational kinetic energy and rolling motion Torque and angular momentum In Figure, in order to turn a rod about a fixed hinge at one end, a force F is applied at a

More information

Chapter 8 Lecture Notes

Chapter 8 Lecture Notes Chapter 8 Lecture Notes Physics 2414 - Strauss Formulas: v = l / t = r θ / t = rω a T = v / t = r ω / t =rα a C = v 2 /r = ω 2 r ω = ω 0 + αt θ = ω 0 t +(1/2)αt 2 θ = (1/2)(ω 0 +ω)t ω 2 = ω 0 2 +2αθ τ

More information

AP Physics C: Rotation II. (Torque and Rotational Dynamics, Rolling Motion) Problems

AP Physics C: Rotation II. (Torque and Rotational Dynamics, Rolling Motion) Problems AP Physics C: Rotation II (Torque and Rotational Dynamics, Rolling Motion) Problems 1980M3. A billiard ball has mass M, radius R, and moment of inertia about the center of mass I c = 2 MR²/5 The ball is

More information

AP Physics 1: Rotational Motion & Dynamics: Problem Set

AP Physics 1: Rotational Motion & Dynamics: Problem Set AP Physics 1: Rotational Motion & Dynamics: Problem Set I. Axis of Rotation and Angular Properties 1. How many radians are subtended by a 0.10 m arc of a circle of radius 0.40 m? 2. How many degrees are

More information

Chapter 9. Rotational Dynamics

Chapter 9. Rotational Dynamics Chapter 9 Rotational Dynamics In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination of translation and rotation. 1) Torque Produces angular

More information

Chapter 9. Rotational Dynamics

Chapter 9. Rotational Dynamics Chapter 9 Rotational Dynamics In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination of translation and rotation. 1) Torque Produces angular

More information

Chapter 9: Rotational Dynamics Tuesday, September 17, 2013

Chapter 9: Rotational Dynamics Tuesday, September 17, 2013 Chapter 9: Rotational Dynamics Tuesday, September 17, 2013 10:00 PM The fundamental idea of Newtonian dynamics is that "things happen for a reason;" to be more specific, there is no need to explain rest

More information

Solution Only gravity is doing work. Since gravity is a conservative force mechanical energy is conserved:

Solution Only gravity is doing work. Since gravity is a conservative force mechanical energy is conserved: 8) roller coaster starts with a speed of 8.0 m/s at a point 45 m above the bottom of a dip (see figure). Neglecting friction, what will be the speed of the roller coaster at the top of the next slope,

More information

Chapter 8. Rotational Equilibrium and Rotational Dynamics

Chapter 8. Rotational Equilibrium and Rotational Dynamics Chapter 8 Rotational Equilibrium and Rotational Dynamics 1 Force vs. Torque Forces cause accelerations Torques cause angular accelerations Force and torque are related 2 Torque The door is free to rotate

More information

Chapter 8. Rotational Motion

Chapter 8. Rotational Motion Chapter 8 Rotational Motion Rotational Work and Energy W = Fs = s = rθ Frθ Consider the work done in rotating a wheel with a tangential force, F, by an angle θ. τ = Fr W =τθ Rotational Work and Energy

More information

Slide 1 / 133. Slide 2 / 133. Slide 3 / How many radians are subtended by a 0.10 m arc of a circle of radius 0.40 m?

Slide 1 / 133. Slide 2 / 133. Slide 3 / How many radians are subtended by a 0.10 m arc of a circle of radius 0.40 m? 1 How many radians are subtended by a 0.10 m arc of a circle of radius 0.40 m? Slide 1 / 133 2 How many degrees are subtended by a 0.10 m arc of a circle of radius of 0.40 m? Slide 2 / 133 3 A ball rotates

More information

Slide 2 / 133. Slide 1 / 133. Slide 3 / 133. Slide 4 / 133. Slide 5 / 133. Slide 6 / 133

Slide 2 / 133. Slide 1 / 133. Slide 3 / 133. Slide 4 / 133. Slide 5 / 133. Slide 6 / 133 Slide 1 / 133 1 How many radians are subtended by a 0.10 m arc of a circle of radius 0.40 m? Slide 2 / 133 2 How many degrees are subtended by a 0.10 m arc of a circle of radius of 0.40 m? Slide 3 / 133

More information

Physics 53 Exam 3 November 3, 2010 Dr. Alward

Physics 53 Exam 3 November 3, 2010 Dr. Alward 1. When the speed of a rear-drive car (a car that's driven forward by the rear wheels alone) is increasing on a horizontal road the direction of the frictional force on the tires is: A) forward for all

More information

Description: Using conservation of energy, find the final velocity of a "yo yo" as it unwinds under the influence of gravity.

Description: Using conservation of energy, find the final velocity of a yo yo as it unwinds under the influence of gravity. Chapter 10 [ Edit ] Overview Summary View Diagnostics View Print View with Answers Chapter 10 Due: 11:59pm on Sunday, November 6, 2016 To understand how points are awarded, read the Grading Policy for

More information

ΣF = ma Στ = Iα ½mv 2 ½Iω 2. mv Iω

ΣF = ma Στ = Iα ½mv 2 ½Iω 2. mv Iω Thur Oct 22 Assign 9 Friday Today: Torques Angular Momentum x θ v ω a α F τ m I Roll without slipping: x = r Δθ v LINEAR = r ω a LINEAR = r α ΣF = ma Στ = Iα ½mv 2 ½Iω 2 I POINT = MR 2 I HOOP = MR 2 I

More information

Name Date Period PROBLEM SET: ROTATIONAL DYNAMICS

Name Date Period PROBLEM SET: ROTATIONAL DYNAMICS Accelerated Physics Rotational Dynamics Problem Set Page 1 of 5 Name Date Period PROBLEM SET: ROTATIONAL DYNAMICS Directions: Show all work on a separate piece of paper. Box your final answer. Don t forget

More information

UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics

UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics Physics 111.6 MIDTERM TEST #2 November 16, 2000 Time: 90 minutes NAME: STUDENT NO.: (Last) Please Print (Given) LECTURE SECTION

More information

Angular Momentum L = I ω

Angular Momentum L = I ω Angular Momentum L = Iω If no NET external Torques act on a system then Angular Momentum is Conserved. Linitial = I ω = L final = Iω Angular Momentum L = Iω Angular Momentum L = I ω A Skater spins with

More information

3. A bicycle tire of radius 0.33 m and a mass 1.5 kg is rotating at 98.7 rad/s. What torque is necessary to stop the tire in 2.0 s?

3. A bicycle tire of radius 0.33 m and a mass 1.5 kg is rotating at 98.7 rad/s. What torque is necessary to stop the tire in 2.0 s? Practice 8A Torque 1. Find the torque produced by a 3.0 N force applied at an angle of 60.0 to a door 0.25 m from the hinge. What is the maximum torque this force could exert? 2. If the torque required

More information

Torque. Introduction. Torque. PHY torque - J. Hedberg

Torque. Introduction. Torque. PHY torque - J. Hedberg Torque PHY 207 - torque - J. Hedberg - 2017 1. Introduction 2. Torque 1. Lever arm changes 3. Net Torques 4. Moment of Rotational Inertia 1. Moment of Inertia for Arbitrary Shapes 2. Parallel Axis Theorem

More information

Chapter 10: Dynamics of Rotational Motion

Chapter 10: Dynamics of Rotational Motion Chapter 10: Dynamics of Rotational Motion What causes an angular acceleration? The effectiveness of a force at causing a rotation is called torque. QuickCheck 12.5 The four forces shown have the same strength.

More information

Rotational Dynamics continued

Rotational Dynamics continued Chapter 9 Rotational Dynamics continued 9.4 Newton s Second Law for Rotational Motion About a Fixed Axis ROTATIONAL ANALOG OF NEWTON S SECOND LAW FOR A RIGID BODY ROTATING ABOUT A FIXED AXIS I = ( mr 2

More information

Chapter 8 Lecture. Pearson Physics. Rotational Motion and Equilibrium. Prepared by Chris Chiaverina Pearson Education, Inc.

Chapter 8 Lecture. Pearson Physics. Rotational Motion and Equilibrium. Prepared by Chris Chiaverina Pearson Education, Inc. Chapter 8 Lecture Pearson Physics Rotational Motion and Equilibrium Prepared by Chris Chiaverina Chapter Contents Describing Angular Motion Rolling Motion and the Moment of Inertia Torque Static Equilibrium

More information

Equilibrium: Forces and Torques

Equilibrium: Forces and Torques Practice 15B Answers are available in the classroom and on the website. Scan this QR code for a direct link. Equilibrium: Forces and Torques 16. Lynn walks across a 9.0 m long plank bridge. The mass of

More information

A) 1 gm 2 /s. B) 3 gm 2 /s. C) 6 gm 2 /s. D) 9 gm 2 /s. E) 10 gm 2 /s. A) 0.1 kg. B) 1 kg. C) 2 kg. D) 5 kg. E) 10 kg A) 2:5 B) 4:5 C) 1:1 D) 5:4

A) 1 gm 2 /s. B) 3 gm 2 /s. C) 6 gm 2 /s. D) 9 gm 2 /s. E) 10 gm 2 /s. A) 0.1 kg. B) 1 kg. C) 2 kg. D) 5 kg. E) 10 kg A) 2:5 B) 4:5 C) 1:1 D) 5:4 1. A 4 kg object moves in a circle of radius 8 m at a constant speed of 2 m/s. What is the angular momentum of the object with respect to an axis perpendicular to the circle and through its center? A)

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Two men, Joel and Jerry, push against a wall. Jerry stops after 10 min, while Joel is

More information

Test 7 wersja angielska

Test 7 wersja angielska Test 7 wersja angielska 7.1A One revolution is the same as: A) 1 rad B) 57 rad C) π/2 rad D) π rad E) 2π rad 7.2A. If a wheel turns with constant angular speed then: A) each point on its rim moves with

More information

The student will be able to: 1 Determine the torque of an applied force and solve related problems.

The student will be able to: 1 Determine the torque of an applied force and solve related problems. Honors Physics Assignment Rotational Mechanics Reading Chapters 10 and 11 Objectives/HW The student will be able to: HW: 1 Determine the torque of an applied force and solve related problems. (t = rx r

More information

Chapter 8 continued. Rotational Dynamics

Chapter 8 continued. Rotational Dynamics Chapter 8 continued Rotational Dynamics 8.6 The Action of Forces and Torques on Rigid Objects Chapter 8 developed the concepts of angular motion. θ : angles and radian measure for angular variables ω :

More information

Angular Momentum L = I ω

Angular Momentum L = I ω Angular Momentum L = Iω If no NET external Torques act on a system then Angular Momentum is Conserved. Linitial = I ω = L final = Iω Angular Momentum L = Iω Angular Momentum L = I ω A Skater spins with

More information

Textbook Reference: Wilson, Buffa, Lou: Chapter 8 Glencoe Physics: Chapter 8

Textbook Reference: Wilson, Buffa, Lou: Chapter 8 Glencoe Physics: Chapter 8 AP Physics Rotational Motion Introduction: Which moves with greater speed on a merry-go-round - a horse near the center or one near the outside? Your answer probably depends on whether you are considering

More information

Cutnell/Johnson Physics

Cutnell/Johnson Physics Cutnell/Johnson Physics Classroom Response System Questions Chapter 9 Rotational Dynamics Interactive Lecture Questions 9.1.1. You are using a wrench in an attempt to loosen a nut by applying a force as

More information

Equilibrium Notes 1 Translational Equilibrium

Equilibrium Notes 1 Translational Equilibrium Equilibrium Notes 1 Translational Equilibrium Ex. A 20.0 kg object is suspended by a rope as shown. What is the net force acting on it? Ex. Ok that was easy, now that same 20.0 kg object is lifted at a

More information

Unit 8 Notetaking Guide Torque and Rotational Motion

Unit 8 Notetaking Guide Torque and Rotational Motion Unit 8 Notetaking Guide Torque and Rotational Motion Rotational Motion Until now, we have been concerned mainly with translational motion. We discussed the kinematics and dynamics of translational motion

More information

6. Find the net torque on the wheel in Figure about the axle through O if a = 10.0 cm and b = 25.0 cm.

6. Find the net torque on the wheel in Figure about the axle through O if a = 10.0 cm and b = 25.0 cm. 1. During a certain period of time, the angular position of a swinging door is described by θ = 5.00 + 10.0t + 2.00t 2, where θ is in radians and t is in seconds. Determine the angular position, angular

More information

Chapter 8 Rotational Motion

Chapter 8 Rotational Motion Chapter 8 Rotational Motion Chapter 8 Rotational Motion In this chapter you will: Learn how to describe and measure rotational motion. Learn how torque changes rotational velocity. Explore factors that

More information

Physics 2210 Homework 18 Spring 2015

Physics 2210 Homework 18 Spring 2015 Physics 2210 Homework 18 Spring 2015 Charles Jui April 12, 2015 IE Sphere Incline Wording A solid sphere of uniform density starts from rest and rolls without slipping down an inclined plane with angle

More information

Rotational Kinetic Energy

Rotational Kinetic Energy Lecture 17, Chapter 10: Rotational Energy and Angular Momentum 1 Rotational Kinetic Energy Consider a rigid body rotating with an angular velocity ω about an axis. Clearly every point in the rigid body

More information

Name Student ID Score Last First. I = 2mR 2 /5 around the sphere s center of mass?

Name Student ID Score Last First. I = 2mR 2 /5 around the sphere s center of mass? NOTE: ignore air resistance in all Questions. In all Questions choose the answer that is the closest!! Question I. (15 pts) Rotation 1. (5 pts) A bowling ball that has an 11 cm radius and a 7.2 kg mass

More information

Wiley Plus. Final Assignment (5) Is Due Today: Before 11 pm!

Wiley Plus. Final Assignment (5) Is Due Today: Before 11 pm! Wiley Plus Final Assignment (5) Is Due Today: Before 11 pm! Final Exam Review December 9, 009 3 What about vector subtraction? Suppose you are given the vector relation A B C RULE: The resultant vector

More information

Review questions. Before the collision, 70 kg ball is stationary. Afterward, the 30 kg ball is stationary and 70 kg ball is moving to the right.

Review questions. Before the collision, 70 kg ball is stationary. Afterward, the 30 kg ball is stationary and 70 kg ball is moving to the right. Review questions Before the collision, 70 kg ball is stationary. Afterward, the 30 kg ball is stationary and 70 kg ball is moving to the right. 30 kg 70 kg v (a) Is this collision elastic? (b) Find the

More information

Rolling, Torque, and Angular Momentum

Rolling, Torque, and Angular Momentum AP Physics C Rolling, Torque, and Angular Momentum Introduction: Rolling: In the last unit we studied the rotation of a rigid body about a fixed axis. We will now extend our study to include cases where

More information

Topic 1: Newtonian Mechanics Energy & Momentum

Topic 1: Newtonian Mechanics Energy & Momentum Work (W) the amount of energy transferred by a force acting through a distance. Scalar but can be positive or negative ΔE = W = F! d = Fdcosθ Units N m or Joules (J) Work, Energy & Power Power (P) the

More information

PHYSICS 221 SPRING EXAM 2: March 30, 2017; 8:15pm 10:15pm

PHYSICS 221 SPRING EXAM 2: March 30, 2017; 8:15pm 10:15pm PHYSICS 221 SPRING 2017 EXAM 2: March 30, 2017; 8:15pm 10:15pm Name (printed): Recitation Instructor: Section # Student ID# INSTRUCTIONS: This exam contains 25 multiple-choice questions plus 2 extra credit

More information

Chapter 8 continued. Rotational Dynamics

Chapter 8 continued. Rotational Dynamics Chapter 8 continued Rotational Dynamics 8.4 Rotational Work and Energy Work to accelerate a mass rotating it by angle φ F W = F(cosθ)x x = rφ = Frφ Fr = τ (torque) = τφ r φ s F to x θ = 0 DEFINITION OF

More information

1301W.600 Lecture 16. November 6, 2017

1301W.600 Lecture 16. November 6, 2017 1301W.600 Lecture 16 November 6, 2017 You are Cordially Invited to the Physics Open House Friday, November 17 th, 2017 4:30-8:00 PM Tate Hall, Room B20 Time to apply for a major? Consider Physics!! Program

More information

PY205N Spring The vectors a, b, and c. are related by c = a b. The diagram below that best illustrates this relationship is (a) I

PY205N Spring The vectors a, b, and c. are related by c = a b. The diagram below that best illustrates this relationship is (a) I PY205N Spring 2013 Final exam, practice version MODIFIED This practice exam is to help students prepare for the final exam to be given at the end of the semester. Please note that while problems on this

More information

Physics 201 Midterm Exam 3

Physics 201 Midterm Exam 3 Physics 201 Midterm Exam 3 Information and Instructions Student ID Number: Section Number: TA Name: Please fill in all the information above. Please write and bubble your Name and Student Id number on

More information

AP Physics. Harmonic Motion. Multiple Choice. Test E

AP Physics. Harmonic Motion. Multiple Choice. Test E AP Physics Harmonic Motion Multiple Choice Test E A 0.10-Kg block is attached to a spring, initially unstretched, of force constant k = 40 N m as shown below. The block is released from rest at t = 0 sec.

More information

1. An object is dropped from rest. Which of the five following graphs correctly represents its motion? The positive direction is taken to be downward.

1. An object is dropped from rest. Which of the five following graphs correctly represents its motion? The positive direction is taken to be downward. Unless otherwise instructed, use g = 9.8 m/s 2 Rotational Inertia about an axis through com: Hoop about axis(radius=r, mass=m) : MR 2 Hoop about diameter (radius=r, mass=m): 1/2MR 2 Disk/solid cyllinder

More information

Equilibrium. For an object to remain in equilibrium, two conditions must be met. The object must have no net force: and no net torque:

Equilibrium. For an object to remain in equilibrium, two conditions must be met. The object must have no net force: and no net torque: Equilibrium For an object to remain in equilibrium, two conditions must be met. The object must have no net force: F v = 0 and no net torque: v τ = 0 Worksheet A uniform rod with a length L and a mass

More information

FALL TERM EXAM, PHYS 1211, INTRODUCTORY PHYSICS I Saturday, 14 December 2013, 1PM to 4 PM, AT 1003

FALL TERM EXAM, PHYS 1211, INTRODUCTORY PHYSICS I Saturday, 14 December 2013, 1PM to 4 PM, AT 1003 FALL TERM EXAM, PHYS 1211, INTRODUCTORY PHYSICS I Saturday, 14 December 2013, 1PM to 4 PM, AT 1003 NAME: STUDENT ID: INSTRUCTION 1. This exam booklet has 14 pages. Make sure none are missing 2. There is

More information

General Definition of Torque, final. Lever Arm. General Definition of Torque 7/29/2010. Units of Chapter 10

General Definition of Torque, final. Lever Arm. General Definition of Torque 7/29/2010. Units of Chapter 10 Units of Chapter 10 Determining Moments of Inertia Rotational Kinetic Energy Rotational Plus Translational Motion; Rolling Why Does a Rolling Sphere Slow Down? General Definition of Torque, final Taking

More information

PHYSICS 220. Lecture 15. Textbook Sections Lecture 15 Purdue University, Physics 220 1

PHYSICS 220. Lecture 15. Textbook Sections Lecture 15 Purdue University, Physics 220 1 PHYSICS 220 Lecture 15 Angular Momentum Textbook Sections 9.3 9.6 Lecture 15 Purdue University, Physics 220 1 Last Lecture Overview Torque = Force that causes rotation τ = F r sin θ Work done by torque

More information

is acting on a body of mass m = 3.0 kg and changes its velocity from an initial

is acting on a body of mass m = 3.0 kg and changes its velocity from an initial PHYS 101 second major Exam Term 102 (Zero Version) Q1. A 15.0-kg block is pulled over a rough, horizontal surface by a constant force of 70.0 N acting at an angle of 20.0 above the horizontal. The block

More information

Chapter 9- Static Equilibrium

Chapter 9- Static Equilibrium Chapter 9- Static Equilibrium Changes in Office-hours The following changes will take place until the end of the semester Office-hours: - Monday, 12:00-13:00h - Wednesday, 14:00-15:00h - Friday, 13:00-14:00h

More information

Announcements Oct 27, 2009

Announcements Oct 27, 2009 Announcements Oct 7, 009 1. HW 14 due tonight. Reminder: some of your HW answers will need to be written in scientific notation. Do this with e notation, not with x signs. a. 6.57E33 correct format b.

More information

t = g = 10 m/s 2 = 2 s T = 2π g

t = g = 10 m/s 2 = 2 s T = 2π g Annotated Answers to the 1984 AP Physics C Mechanics Multiple Choice 1. D. Torque is the rotational analogue of force; F net = ma corresponds to τ net = Iα. 2. C. The horizontal speed does not affect the

More information

= y(x, t) =A cos (!t + kx)

= y(x, t) =A cos (!t + kx) A harmonic wave propagates horizontally along a taut string of length L = 8.0 m and mass M = 0.23 kg. The vertical displacement of the string along its length is given by y(x, t) = 0. m cos(.5 t + 0.8

More information